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The gas mileage for a car is 23 miles per gallon when the car travels at 60 miles per hour. The car begins a trip with 13 gallons in its tank, travels at an average speed of 60 miles per hour for 
h hours, and ends the trip with 10 gallons in its tank. Which of the following equations best models this situation?
Choose 1 answer:

13-(23 h)/(60)=10

13-(60 h)/(23)=10

(13-60 h)/(23)=10

(13-23 h)/(60)=10

The gas mileage for a car is 2323 miles per gallon when the car travels at 6060 miles per hour. The car begins a trip with 1313 gallons in its tank, travels at an average speed of 6060 miles per hour for h h hours, and ends the trip with 1010 gallons in its tank. Which of the following equations best models this situation?\newlineChoose 11 answer:\newline(A) 1323h60=10 13-\frac{23 h}{60}=10 \newline(B) 1360h23=10 13-\frac{60 h}{23}=10 \newline(C) 1360h23=10 \frac{13-60 h}{23}=10 \newline(D) 1323h60=10 \frac{13-23 h}{60}=10

Full solution

Q. The gas mileage for a car is 2323 miles per gallon when the car travels at 6060 miles per hour. The car begins a trip with 1313 gallons in its tank, travels at an average speed of 6060 miles per hour for h h hours, and ends the trip with 1010 gallons in its tank. Which of the following equations best models this situation?\newlineChoose 11 answer:\newline(A) 1323h60=10 13-\frac{23 h}{60}=10 \newline(B) 1360h23=10 13-\frac{60 h}{23}=10 \newline(C) 1360h23=10 \frac{13-60 h}{23}=10 \newline(D) 1323h60=10 \frac{13-23 h}{60}=10
  1. Gas Usage Calculation: We need to determine how much gas the car uses over hh hours when traveling at 6060 miles per hour. The car's gas mileage is 2323 miles per gallon, which means for every hour the car travels at 6060 miles per hour, it uses 6023\frac{60}{23} gallons of gas. Since the car starts with 1313 gallons and ends with 1010 gallons, the amount of gas used is 1310=313 - 10 = 3 gallons. We need to find the value of hh that corresponds to this usage.
  2. Equation Setup: To find the number of hours hh that the car traveled, we can set up an equation where the total gallons used (1310)(13 - 10) equals the gallons used per hour (60/23)(60/23) times the number of hours hh. This gives us the equation 13(6023)h=1013 - \left(\frac{60}{23}\right)h = 10.
  3. Equation Verification: We can check the equation by plugging in the values. If hh is the number of hours the car traveled, then (6023)h(\frac{60}{23})h should give us the number of gallons used. Since the car used 33 gallons (1310)(13 - 10), we can check if (6023)h(\frac{60}{23})h equals 33 when hh is the correct number of hours. If we solve the equation for hh, we should get a reasonable number that, when multiplied by (6023)(\frac{60}{23}), gives us 33.

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